~ A blog about IQ, the brain & success

Do Brain Size readers really have an average IQ of 147?

My recent post about how readers of brainsize.wordpress.com have an average IQ of 147 was damaging to the self-esteem of many readers. For example a reader named “Andrew” wrote:

I suppose I’m the dunce around here with an IQ of ~120!

Intelligence is relative, so even though an IQ of 120 is higher than 90% of the U.S. population, when you find yourself on a blog like this one where the average IQ is said to be 147, an IQ of 120 can feel extremely low.

Well the good news for all the “Andrews” out there is that my readers do not have an average IQ of 147 after all. That figure was arrived at using remarkabley indirect evidence. A poll I conducted found that the average reader was about 0.62 standard deviations taller than others of their demographic group, and since height is thought to correlate 0.2 with IQ, I simply dividing their average height (+0.62 SD) by 0.2, to estimate their average IQ to be 3.1 SD above the mean (IQ 147).

There were a couple problems with this however. For starters, as more readers have started to vote in the height poll, it seems the average reader is 0.43 SD taller than normal, not 0.62 SD as previously estimated. Secondly, while 0.2 is the correlation between IQ and height, what I really want is the correlation between height and g (general intelligence) and I want it corrected for reliability. This figure would be about 0.26.

So now with the revised height (+0.43 SD) divided by the true g loading of height (0.26), it seems Brain Size readers have an average general intelligence of 1.65 SD above normal. In other words, Brain Size readers average an IQ of 125. This is a far more believable figure than 147, which is about what you’d expect from the average academic Nobel Prize winner.

Many people are confused by why I divided the height of my readers (+0.43 SD) by the true g loading of height (0.26), instead of just multiplying it. For example, NBA players are ridiculously tall (perhaps +3.88 SD taller than other American men in their age group). If I wanted to estimated the average IQ of NBA players from their average height, would I divide their height by the g loading of height? If so, their estimated intelligence would be +14.92 SD (an average deviation IQ of 324 making the average NBA player more than 100 IQ points smarter than any person who ever lived!) So instead of dividing their height (+3.88 SD) by 0.26, I would multiply, which gives an estimated intelligence of +1 SD (IQ 115).

The height poll still do not have a proper normal distribution. So I would be more patient for more votes to draw a conclusion…

A perfect Gaussian distribution is an abstraction seldom perfectly observed.

Or maybe it does not matter results not having a normal distribution?

Regression depends on the assumption that distributions are roughly normal.

Another reason might be that some were not that honest with the vote 🙂

There’s little incentive to lie about your height in an anonymous poll although a lot of men are in great denial about their height, and even more so about their IQ.

But whatever extent the poll results would be inflated by overestimates of one’s height would likely be cancelled out by voters who come from shorter demographic groups than I used as a reference group (white men under 40)

additionally, 147 is the average score of a high range IQ test taker. It is not impossible.

There are a lot of people who are very interested in IQ & read & blog about IQ, who would never dare take one of those high range tests because just looking at them, it’s obvious they would fail, so the people who take those tests might be extremely self-selected, even among IQ junkies.

“who would never dare take one of those high range tests because just looking at them, it’s obvious they would fail,”

Indeed, ignorance is bliss. Also true for aged people in denial of their age, terminally-illed patients in denial of their disease, idiots in denial of their stupidity, losers in denial of their defeat or failure. The list can go on and on.

Another way to estimate people’s intelligence based on verbal conversation is see whether they can differentiate opinion vs fact (truth).

The people who can clearly differentiate them usually have IQ above 125 which is needed for scientific activities.

Most people including those with average intelligence have hard time differentiating them.

Your new number (IQ125) is much more in line with people of science. You can see that some with strong math ability corrects your mistake. In other word, people of strong math are strong in abstract thinking (high IQ).

This is also helpful to resolve the conflict height vs longevity, height vs IQ, IQ vs longevity issue. If you do calculation with above principle, you will find that IQ correlation with longevity overpower height correlation with longevity: height correlation with IQ is pretty weak therefore. If height correlation with IQ were stronger, the you would have high IQ people with reduced longevity.

Why are you dividing or multiplying the SD height difference by correlation to obtain the IQ estimate? What equation or formula is this based on?
You say that the avg height of the poll takers was +0.43 SD and this corresponds to an estimated IQ of 125. Had the avg height been greater the IQ would have been greater (and it rises very steeply because dividing by .26 is the same as multiplying by its reciprocal which is about 3.85). So 1 SD increase in height means 3.85 SD increase in IQ.
+ 2 SD in height is + 7.7 SD in IQ which would mean IQ of 216 or so.
Since one obtains ridiculous IQ values very quickly in this way, you would suggest multiplying the height SD by correlation instead of dividing by it after certain value of height (otherwise nonsensical IQ estimates will inevitably result).
In this way the NBA players’ IQ estimate came out to be 115.
Do you see how if we were to graph this height-IQ graph you’d see a straight line with a slope of 3.85 continuing to rise to a certain extent and then drop suddenly to some much lower value then continue to rise again but this time at a much smaller slope of .26?
In other words the graph would rise very steeply up to a certain point then fall precipitously and then start rising again but this time much more gradually.
This is a very odd graph purportedly showing the relationship btw height and estimated IQ. Your method of estimating IQ solely based on height seem very spurious to me to say the least and raises many unanswerable questions.

Aren’t the points I raised valid Pumpkinperson? Or did I misunderstand your method? What equations, formulas, relationships, definitions, concepts is your IQ extrapolation method based on? I ask this in large part out of pure intellectual curiosity. Yes I am skeptical of what you purported to show but maybe I misunderstood something. So please enlighten me if I was mistaken. I’m no expert on psychometrics or statistics but I did major in math at a solid university and have passed the preliminary actuarial exams which are based on basic probability and stat.

Sorry this blog has moved to pumpkinperson.com so I’ve been busy over there.

If the correlation between X and Y is r, then in a standardized bivariate normal distribution, you can estimate the average level on trait X for people who are selected for trait Y by multiplying Y by r. You can also estimate the average level on trait Y for people who are selected for trait X by multiplying X by r.

Thus, if you know that people are only high on X because they were selected by Y or if you know that they are high on Y because they were selected by X, you can reason backwards and divide by r instead to estimate the amount of selection on the primary trait

“If the correlation between X and Y is r, then in a standardized bivariate normal distribution, you can estimate the average level on trait X for people who are selected for trait Y by multiplying Y by r.”

Can you cite sources that back this up such as chapters in textbooks? Better yet produce series of equations that prove this or at least direct us to websites that have proof of this? If this is valid reasoning then there should be plenty of sites that explain this mathematically step by step.

I didn’t major in prob/stat and I forgot much of even the basic prob/stat stuff I learned in college through years of disuse but I have enough intelligence and patience to relearn them if needed. I have a few undergrad textbooks on probability theory and mathematical statistics at home that I looked through just to refresh my memory but I cannot find what supports the validity of your method. I don’t see how it follows from the definition of correlation.

Furthermore it seems highly improbable intuitively that one can extrapolate a meaningful estimate of an avg IQ of a group of ppl based on their heights alone. In fact I find this ludicrous quite frankly. The correlation btw height and IQ is quite low in the order of 0.2 according to Gene Expression. The lower the correlation the less we would be able to come up with valid predictions. But according to your reasoning the effect of decreasing correlation is increase in the estimated IQ of the group. The lower the correlation the less the meaningfulness of the estimated value of IQ. If say for the sake of argument we were to assume that the correlation btw height and IQ was 0.1, your method would produce 6.2 SD above the mean IQ.

Why should lowering of the value of correlation have the effect of increasing the estimated value of IQ?
Shouldn’t lower correlation mean lowered ability to come up with a meaningful estimate instead?

A less misleading way to think about the correlation R is as follows: given X,Y from a standardized bivariate distribution with correlation R, an increase in X leads to an expected increase in Y: dY = R dX. In other words, students with +1 SD SAT score have, on average, roughly +0.4 SD college GPAs. Similarly, students with +1 SD college GPAs have on average +0.4 SAT.

If you don’t believe us, simply take pairs of normally distributed data, convert it into Z scores, create a scatter plot relating X to Y, and observe whether the slope of the line of best fit matches the correlation: it should come quite close.

Why should lowering of the value of correlation have the effect of increasing the estimated value of IQ?

Because if the indicator of intelligence is so weak, and yet the group (selected for intelligence, not the indicator of intelligence) still scored high on it, then the group’s intelligence would have to be that much higher to overcome the low signal/noise ratio.